It took my code to setup the problem 10 seconds more than cvx.
cvx eliminated 3/5 of the constraints.
After factorization cvx had 2.9e5 nnz vs. 1.4e8 nnz in mine.
This leads to mosek solution of 1.3 seconds for cvx formulation, while for my formulation I stopped it on the fourth iteration after 183 seconds.
I should note that mosek eliminated variables for my formulation, which means that cvx does a better job at it.